единственность решения

A Couple Contact Loading at the Unilateral Contact of Beams

Authors: Osipenko M. A., Kasatkin A. A.

The contact problem for the structure consisting of two beams is considered. The beams have the different lengths and the different variable thicknesses. One end of the shorter beam is clamped coinciding with the hinge dend of the longer beam.The other ends of the beams are free. The given loading is applied to the longer beam. The beams undergo the weak joint bending with the unilateral (receding) contact. There is no friction between the beams.The bending of each beam is described by Bernoulli–Eulermodel.The contact problem is to find the contact loading, i.e.

Weakly Ill-posed Problems of Integral Geometry witch Perturbation on Polygonal Lines

Authors: Begmatov A. H., Pirimbetov A. O., Seidullaev A. K.

We study a problem of reconstruction of a function in a strip from their given integrals with known weight function along polygonal lines. We obtained two simply inversion formulas for the solution to the problem. Using these representations we prove uniqueness and existence theorems for solutions and obtain stability estimates of a solution to the problem in Sobolev’s spaces and thus show their weak ill-posedness. Then we consider integral geometry problems with perturbation. The uniqueness theorems are proved and stability estimates of solutions in Sobolev spaces are obtained.